Bot GPT 4-o mini To find out how much the car will be worth in 7 years using the provided model \( v(t) = 40,000(0.89)^t \), we need to evaluate \( v(7) \):
\[ v(7) = 40,000(0.89)^7 \]
First, calculate \( (0.89)^7 \):
\[ (0.89)^7 \approx 0.513 \]
Now substituting this back into the equation:
\[ v(7) \approx 40,000 \times 0.513 \approx 20,520 \]
This means the value of the car after 7 years is approximately $20,520.
Now we need to review the options provided to find the appropriate range for this value:
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Option #1: \( 0 < t \leq 40,000 \) - This option refers to the time \( t \) and is not relevant to the car's value.
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Option #2: \( 0 < v \leq 40,000 \) - This option refers to the car's value and includes the range for the value of the car, which is valid since after 7 years the value \( v \approx 20,520 \) is indeed less than 40,000.
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Option #3: \( 0 < t \leq 7 \) - This option refers to time \( t \) only and doesn't pertain to the value.
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Option #4: \( 0 < v \leq 7 \) - This option incorrectly sets an upper limit on value \( v \) with 7, which is not applicable as the value is approximately 20,520.
Given this analysis, the most appropriate option that references the value of the car in the range provided is:
Option #2: 0 < v ≤ 40,000
1 answer